fast_cos_cheby.jl

c_0 = -0.969474842881623111168210
c_2 = 4.364528972627628178315717
c_4 = -2.422793242101592081638728 

function fast_cos(t::Real)
    # Computes cos(pi*t) using a Chebyshev approximation.
    # This approximation is minimax optimal on [-1, 1].
    # By scaling by pi, we find an optimal approximation on
    # the entire range of cos(x). Because cos(x - pi) = -cos(x),
    # we can take the remainder with 2, and shift [0, 2] |-> [-1, 1],
    # taking the negative of the coefficients to compute -cos(x)
    # instead. This is a 4th order approximation.
    cos_t::Real;
    t = rem(t, 2.0) - 1.0;
    cos_t = c_0 + c_2 * t^2 + c_4 * t^4;
    return cos_t;
end